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2 years ago

How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10? triangle(s)

Mathematics

1 answer:

Shalnov [3]2 years ago

5 0

Using the law of sines, it is found that 1 triangle can be formed with the given conditions.

<h3>What is the law of sines?</h3>

Suppose we have a triangle in which:

The length of the side opposite to angle A is a.

The length of the side opposite to angle B is b.

The length of the side opposite to angle C is c.

The lengths and the sine of the angles are related as follows:

$\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}$

Hence, for this problem, we have that the relation is:

$\frac{\sin{64^\circ}}{10} = \frac{\sin{G}}{9}$

$\sin{G} = 0.9\sin{64^\circ}$

$\sin{G} = 0.8089$

$G = \arcsin{0.8089}$

G = 54º

A triangle can have one angle of 64º and another of 54º, hence 1 triangle can be formed with the given conditions.

More can be learned about the law of sines at brainly.com/question/25535771

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Which of the following statements must be true based on the diagram below?

liubo4ka [24]

Answer: CG is a segment bisector.

Step-by-step explanation:

A segment bisector splits a segment into two equal parts. Notice the marks on FG and GE. The marks are showing that FG and GE are of equal length, therefore CG is bisecting segment FE into two equal segments.

3 0

3 years ago

Consider the function f(x) = x2 + 2x – 15. What are the x-intercepts of the function?

Rus_ich [418]

Answer:

The x-intercepts of the function are $x = 3$ and $x = -5$ .

Step-by-step explanation:

We are given the function $\displaystyle f(x) = x^2 + 2x - 15$ .

In order to find the x-intercepts of the equation, we need to solve this quadratic. We can use factoring methods to solve it.

The parent function for a quadratic is $f(x) = ax^2 + bx + c = 0$ .

We can use this information to determine what factoring technique we want to use.

There are several different methods, including using the quadratic formula, but because this is easily factorable, we can avoid using it.

We see that our <em>a</em> is equal to 1 (there is no coefficient in front of x²), so we can use the easier of the techniques:

Find what factors of c add up to give you b.
Add to x if positive or subtract from x if negative and set it equal to zero.
Solve for x - these are your x-intercepts.

Therefore, let's determine what our c is: 15.

Now, let's label the factors for 15.

15 cannot be divided by 2 evenly.
15 can be divided by 3 evenly: 15/3 = 5
15 cannot be divided by 4 evenly.
15 can be divided by 5 evenly: 15/5 = 3

Therefore, our two factors are 3 and 5 since they cannot be broken down any further (they are prime numbers - we just performed prime factorization).

Now, we need to pay attention to the sign for c. It's negative, so one of our factors needs to be negative. Therefore, we can test this out:

$5 + -3 = 2$
$-5 + 3 = -2$

Now, we check for which one matches the sign for b. This is positive 2, so our two factors are 5 and -3.

Finally, to factor, we add or subtract the factors from x depending on the sign. If the factor is positive, we add it. If the factor is negative, we subtract it. Therefore, we can set up our equations.

$x + 5 = 0\\\\x = -5$

$x - 3 = 0\\\\x = 3$

Therefore, for when x = 3 or x = -5, the line crosses the x-axis. These are the x-intercepts of the function.

Our answers are x = -5 and x = 3.

4 0

3 years ago

Which situation can be represented by this inequality?

MaRussiya [10]

The true option is: (d) <em>Hugo has 15 songs in his music player. He will add 10 songs every month. Hugo collects songs for r months. For what values of r will Hugo have at least 135 songs?</em>

The inequality is given as:

$\mathbf{135 \le 10r + 15}$